%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:39:33 PM UTC 2026
% Result : Unsatisfiable 0.17s 1.21s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 13 unt; 2 def)
% Number of atoms : 44 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 14 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : member(X0,singleton_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ member(X0,singleton_set(X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_2) ).
fof(f3,axiom,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_1) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_3) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f7,axiom,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pairs) ).
fof(f8,negated_conjecture,
m1 != m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_first_components_equal) ).
fof(f9,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
inference(definition_unfolding,[],[f7,f6,f6]) ).
fof(f15,plain,
member(singleton_set(m2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(superposition,[],[f3,f9]) ).
fof(f16,plain,
( singleton_set(m1) = singleton_set(m2)
| unordered_pair(m1,r1) = singleton_set(m2) ),
inference(resolution,[],[f15,f5]) ).
fof(f18,definition,
( spl0_1
<=> unordered_pair(m1,r1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f19,plain,
( unordered_pair(m1,r1) = singleton_set(m2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f21,definition,
( spl0_2
<=> singleton_set(m1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f22,plain,
( singleton_set(m1) = singleton_set(m2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f23,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f16,f21,f18]) ).
fof(f27,plain,
( member(m2,singleton_set(m1))
| ~ spl0_2 ),
inference(superposition,[],[f1,f22]) ).
fof(f36,plain,
( m1 = m2
| ~ spl0_2 ),
inference(resolution,[],[f27,f2]) ).
fof(f37,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f36,f8]) ).
fof(f38,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f37]) ).
fof(f50,plain,
( member(m1,singleton_set(m2))
| ~ spl0_1 ),
inference(superposition,[],[f3,f19]) ).
fof(f69,plain,
( m1 = m2
| ~ spl0_1 ),
inference(resolution,[],[f50,f2]) ).
fof(f70,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f69,f8]) ).
fof(f71,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f70]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f38]) ).
cnf(s6,plain,
~ spl0_1,
inference(sat_conversion,[],[f71]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s3,s6]) ).
fof(f72,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n016.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 00:11:03 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/1.21 % (3139188)Input is clausal, will run a generic CNF schedule.
% 0.17/1.21 % (3139196)lrs+10_1_sil=8000:sp=occurrence:random_seed=600898154:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/1.21 % (3139193)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1782486429:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.17/1.21 % (3139195)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=164117260:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.17/1.21 % (3139194)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2699044175:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.17/1.21 % (3139197)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3661671953:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.17/1.21 % (3139199)dis-21_1_sil=8000:lcm=predicate:random_seed=94690339:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.17/1.21 % (3139198)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3517891914:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/1.21 % (3139199)Refutation not found, incomplete strategy
% 0.17/1.21 % (3139199)------------------------------
% 0.17/1.21 % (3139199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.21 % (3139199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.21 % (3139199)CaDiCaL version: 2.1.3
% 0.17/1.21 % (3139199)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.21 % (3139199)Time elapsed: 0.001 s
% 0.17/1.21 % (3139199)Peak memory usage: 88 MB
% 0.17/1.21 % (3139197)First to succeed.
% 0.17/1.21 % (3139196)Also succeeded, but the first one will report.
% 0.17/1.21 % (3139197)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3139188"
% 0.17/1.21 % (3139198)Also succeeded, but the first one will report.
% 0.17/1.21 % (3139199)------------------------------
% 0.17/1.21 % (3139199)------------------------------
% 0.17/1.21 % (3139197)Refutation found. Thanks to Tanya!
% 0.17/1.21 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.21 % (3139197)------------------------------
% 0.17/1.21 % (3139197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.21 % (3139197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.21 % (3139197)CaDiCaL version: 2.1.3
% 0.17/1.21 % (3139197)Termination reason: Refutation
% 0.17/1.21 % (3139197)Time elapsed: 0.003 s
% 0.17/1.21 % (3139197)Peak memory usage: 89 MB
% 0.17/1.21 % (3139197)Instructions burned: 2 (million)
% 0.17/1.21 % (3139197)------------------------------
% 0.17/1.21 % (3139197)------------------------------
% 0.17/1.21 % (3139188)Success in time 0.385 s
% 0.17/1.21 % Vampire exiting
%------------------------------------------------------------------------------